Expanding Spacetime - Inside an Atom?

I think that it is correct to say that everywhere, spacetime is expanding.

Is it expanding within the radius of electrons within atoms? Are the radii getting larger over time?

I believe it correct that the distance from the nucleus to an electron exceeds the diameter of either one by many orders of magnitude. So mostly the volume of an atom is composed of "empty space". Is that stuff in those locations expanding like any normal intergalactic space?

To the best of our knowledge, atoms do not partake in the expansion of the universe. The radius of an atom is proportional to the Bohr radius, ħ2/me2, and this depends only on the fundamental constants of nature. To considerable accuracy, these have not changed over the lifetime of the universe.

To the best of our knowledge, atoms do not partake in the expansion of the universe. The radius of an atom is proportional to the Bohr radius, ħ2/me2, and this depends only on the fundamental constants of nature. To considerable accuracy, these have not changed over the lifetime of the universe.

That makes sense, given that physical objects do not grow lager as the universe expands.

But I can't understand why not. What is different about the spacetime in the proximity of matter, making it such that it does not expand along with intergalactic space?

I didn't say the spacetime inside an atom was different. What I said was, the atom itself does not expand. The electron and nucleus are not pegged to particular locations in space and dragged along by the cosmic expansion. The atom remains the same size because the mass of the electron remains the same, and the electric field of the nucleus remains the same, so they remain (on average) a constant distance apart.

The same reasoning applies to any bound system, even a galaxy or a cluster of galaxies. They don't expand either.

Anything bound by any of the fundamental forces will overcome the expansion of the universe. This includes gravity, which is extremely weak. The expansion of the universe is even weaker.

The gravity within galaxies, and even between galaxies is easily strong enough to overwhelm the expansion. That's why the only place we observe this expansion is on huge scales, such as between galaxy clusters, where gravity is infinitesimally small.

Think of this thought experiment. Tape a dozen pennies in random places on a partially inflated balloon, then blow up the balloon. Do the pennies get larger? No. The forces holding each penny together are far, far larger than the expansion of the balloon.

The answer to the question isn't really known. For example in an Einstein-Strauss model, expansion only takes place place outisde of the vacuoles. As the vacuoles in this model are meant to represent stars and their surrounding space, in this model expansion only takes place inbetween stars.

However I think recently (the last decade or two) some criticisms have been made of the Einstein-Strauss model which means it should not be taken as a serious physical model of the Universe and secondly the model was conceived long before dark energy was postulated.

We might reasonably expect dark energy to act as a general repulsive influence on scales even as small as the atomic, on the other hand we have no way of knowing that that is the case.

All this just goes to underline the fact that it is still an open question in cosmology as to what exactly is the effect of expansion on scales smaller than what might be called 'cosmologically significant'.